BASIC METEOROLOGICAL PROCESSES

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BASIC
METEOROLOGICAL
PROCESSES

Objectives


What is atmospheric thermodynamics?


What are the variables of atmospheric thermodynamics?


What is lapse rate?


Explain the potential temperature.


What is atmospheric stability and the various methods that
define atmospheric stability?


What is boundary layer development?


What are the effects of meteorology on plume dispersion?


What is wind velocity profile?


What is wind rose diagram and what are the uses of it?


Determination of mixing height.

A
IR

P
OLLUTION

M
ETEOROLOGY


Atmospheric thermodynamics



Atmospheric stability



Boundary layer development



Effect of meteorology on plume dispersion


A
TMOSPHERE


Pollution

cloud

is

interpreted

by

the

chemical

composition

and

physical

characteristics

of

the

atmosphere


Concentration

of

gases

in

the

atmosphere

varies

from

trace

levels

to

very

high

levels


Nitrogen

and

oxygen

are

the

main

constituents
.

Some

constituents

such

as

water

vapor

vary

in

space

and

time
.


Four

major

layers

of

earth’s

atmosphere

are
:


Troposphere


Stratosphere


Mesosphere


Thermosphere


A
TMOSPHERIC

T
HERMODYNAMICS


A parcel of air is defined using the state variables


Three important state variables are density, pressure
and temperature


The units and dimensions for the state variables are



Density

(mass/volume)


gm/cm
3


ML
-
3

Pressure (Force/Area)


N/m
2
( P
a
)


ML
-
1
T
-
2

Temperature

o
F,
o
R,
o
C,

o
K



T


Humidity is the fourth important variable that gives the
amount of water vapor present in a sample of moist air

E
QUATION

OF

S
TATE


Relationship between the three state variables may be
written as:


f ( P, ρ ,T) = 0



For a perfect gas:


P = ρ .R .T


R is Specific gas constant


R for dry air = 0.287
Joules / gm /
o
K



R for water vapor = 0.461 Joules / gm /
o
K




R for wet air is not constant and depend on mixing ratio

Exercise


Calculate the density of a gas with a molecular weight of 29 @ 1
atm (absolute) and 80
o
F. Gas constant, R = 0.7302 ft
3
atm/lb
-
mole
o
R.

Solution

Absolute Temperature = 80
o
F + 460 = 540
o
R

Density = P ( molecular weight) / RT

Density = ( 1atm. )*(29 lb/lb mole) / ( 0.7302 ft
3
atm/lb
-
mole
o
R)*(540
o
R)

Density = 0.073546 lb/ ft
3
.

Exercise


Determine the pressure, both absolute and gauge, exerted at the
bottom of the column of liquid 1 meter high, with density of 1000
kg / m3.


Solution


Step 1

:

Pgauge = (density of liquid) * ( acceleration due to gravity)




*(height of liquid column)

Step 2

:

Pabsolute = Pgauge + Patmospheric




Pabsolute = 111.11 kPa

L
AWS

OF

T
HERMODYNAMICS

First Law of Thermodynamics:


This law is based on law of conservation of total energy.


Heat added per unit mass =
(Change in internal energy per unit mass)

+ (Work done by a unit mass)




δH = δU+δW


Second Law of Thermodynamics:


This law can be stated as "no cyclic process exists having the
transference of heat from a colder to hotter body as its sole
effect"

S
PECIFIC

H
EAT


Defined as the amount of heat needed to change the
temperature of unit mass by 1
o
K.



Specific heat at constant volume



C
v
= lim
δQ


δT

0 δT
α = const





Specific heat at constant pressure



C
p
= lim
δQ


δT

0 δT
p = const


Relationship between C
v
and C
p
is given by Carnot’s law:




For perfect gas, C
p


C
v
= R



For dry air C
p

= (7/2)*R (Perfect diatomic gas)


C
v
= (5/2)*R (Perfect diatomic gas)



Ratio of C
p

and C
v

for dry air is 1.4

C
pd

= 1.003 joules/gm/
o

K ;
C
vd


= 0.717 joules/gm/
o

K

P
ROCESSES

IN

THE

A
TMOSPHERE


An air parcel follows several different paths when it
moves from one point to another point in the
atmosphere. These are:


Isobaric change



constant pressure


Isosteric change



constant volume


Isothermal change



constant temperature


Isentropic change



constant entropy (E)


Adiabatic Process



δQ = 0
(no heat is added or


removed )



The adiabatic law is P. α
γ
= constant


E =

S
TATICS

OF

THE

A
TMOSPHERE


Vertical variation of the parameters = ?

Hydrostatic Equation:


Pressure variation in a "motionless" atmosphere





Pressure variation in an atmosphere:





Relationship between pressure and elevation using gas law:

S
TATICS

OF

THE

A
TMOSPHERE


Integration of the above equation gives




Using the initial condition Z=0, P = P
0


The above equation indicates that the variation of
pressure depends on vertical profile of temperature.


For iso
-
thermal atmosphere




Therefore, pressure decreases exponentially with
height at a ratio of 12.24 mb per 100m.


Lapse Rate:


Lapse rate is the rate of change of temperature with
height


Lapse rate is defined as Γ =
-
δT


δz


Value of


Γ varies throughout the atmosphere



Potential Temperature:


Concept of potential temperature is useful in comparing two air
parcels at same temperatures and different pressures.

C
ONCEPT

OF

P
OTENTIAL

T
EMPERATURE

θ

A
TMOSPHERE

S
TABILITY


The ability of the atmosphere to enhance or to resist
atmospheric motions



Influences the vertical movement of air.



If the air parcels tend to sink back to their initial level after
the lifting exerted on them stops, the atmosphere is
stable
.



If the air parcels tend to rise vertically on their own, even
when the lifting exerted on them stops, the atmosphere is
unstable
.



If the air parcels tend to remain where they are after lifting
stops, the atmosphere is
neutral
.


A
TMOSPHERIC

S
TABILITY


The stability depends on the ratio of suppression to
generation of turbulence



The stability at any given time will depend upon static
stability ( related to change in temperature with height ),
thermal turbulence ( caused by solar heating ), and
mechanical turbulence (a function of wind speed and
surface roughness).


A
TMOSPHERIC

S
TABILITY


Atmospheric stability can be determined using adiabatic
lapse rate.


Γ >
Γ
d


Unstable


Γ = Γ
d


Neutral


Γ <
Γ
d


Stable


Γ is environmental lapse rate


Γ
d

is dry adiabatic lapse rate (1
0
c/100m) and
dT
/
dZ

=
-
1
0
c /100 m

A
TMOSPHERIC

S
TABILITY

C
LASSIFICATION


Schemes to define atmospheric stability are:



P
-

G Method



P
-
G / NWS Method



The STAR Method



BNL Scheme



Sigma Phi Method



Sigma Omega Method



Modified Sigma Theta Method



NRC Temperature Difference Method



Wind Speed ratio (U
R
) Method


Radiation Index Method


AERMOD Method (Stable and Convective cases)

P
ASQUILL
-
GIFFORD

S
TABILITY

C
ATEGORIES

Surface Wind

Speed (m/s
)

Daytime Insolation

Nighttime cloud
cover

Strong

Moderate

Slight

Thinly
overcast or 4/8
low cloud

3/8

< 2

A


A
-

B

B

-

-

2
-

3

A
-

B

B

C

E

F

3
-

5

B

B
-

C

C

D

E

5
-

6

C

C
-

D

D

D

D

> 6

C

D

D

D

D

Source: Met Monitoring Guide


Table 6.3

S
IGMA

T
HETA

STABILITY

CLASSIFICATION

CATEGORY

PASQUILL CLASS

SIGMA THETA (ST)

EXTREME UNSTABLE

A

ST>=22.5

MODERATE UNSTABLE

B

22.5>ST>=17.5

SLIGHTLY UNSTABLE

C

17.5>ST>=12.5

NEUTRAL

D

12.5>ST>=7.5

SLIGHTLY STABLE

E

7.5>ST>= 3.8

MODERATE STABLE

F

3.8>ST>=2.1

EXTREMELY STABLE

G

2.1>ST


Source: Atmospheric Stability


Methods & Measurements (NUMUG
-

Oct 2003)

T
EMPERATURE

D
IFFERENCE

(∆T)

Source: Regulatory guide; office of nuclear regulatory research
-

Table 1

T
URBULENCE


Fluctuations in wind flow which have a frequency of
more than 2 cycles/ hr



Types of Turbulence


Mechanical Turbulence


Convective Turbulence


Clear Air Turbulence


Wake Turbulence

L
OCAL

CLIMATOLOGICAL
DATA

-

T
OLEDO

W
EATHER

CONDITIONS

OF

TOLEDO


Weather Station


Home, Professional, and Live

Weather Balloon


Pressure, Temperature, Wind Speed, Wind Direction, &
Humidity

Use of Towers


Velocity, Temperature, & Turbulence

L
OCAL

CLIMATOLOGICAL
DATA

-

T
OLEDO


Greatest snowfall


73.1” (1997
-
1998)


Least snowfall


6.0” (1889
-
1890)


Average number of days with a tenth of an inch or more
snowfall


27 days

Annual

38.3”

D散emb敲

9.1”

January

9.8”

䙥Fruary

8.0”

䵡r捨

6.3”

Snowfall

Annual

49.6
°
F

January

25.7
°
F

July

73.2
°
F

Temperature

Annual

31.62”

䩡nuary

2.18”

䩵ne

3.45”

Precipitation

National Weather Map


US Forecast

National Air Quality


Ozone

Climate


Temperature

N
ATIONAL

W
EATHER

M
AP

H


High Pressure Area

L


Low Pressure Area


A high pressure area forecasts clear skies.


A low pressure area forecasts cloudiness and precipitation


B
OUNDARY

L
AYER

D
EVELOPMENT

B
OUNDARY

L
AYER

D
EVELOPMENT


Thermal boundary Layer (TBL) development depends on
two factors:


Convectively produced turbulence


Mechanically produced turbulence



Development of TBL can be predicted by two distinct
approaches:



Theoretical approach



Experimental studies

B
OUNDARY

L
AYER

D
EVELOPMENT


Theoretical approach may be classified into three
groups:


Empirical formulae


Analytical solutions


Numerical models



One layer models



Higher order closure models


TBL
USING

A
NALYTICAL

S
OLUTION


Time

Time

Time

Time

E
FFECTS

OF

M
ETEOROLOGY

ON

P
LUME

D
ISPERSION

E
FFECTS

OF

M
ETEOROLOGY

ON

P
LUME

D
ISPERSION


Dispersion of emission into atmosphere depends on
various meteorological factors.



Height of thermal boundary layer is one of the
important factors responsible for high ground level
concentrations



At 9 AM pollutants are pulled to the ground by
convective eddies



Spread of plume is restricted in vertical due to thermal
boundary height at this time

W
IND

V
ELOCITY


A power law profile is used to describe the variation of
wind speed with height in the surface boundary layer



U = U
1
(Z/Z
1
)
p

Where,


U
1

is the velocity at Z
1

(usually 10 m)


U is the velocity at height Z.

The values of p are given in the following table.


Stability Class

Rural p

Urban p

Very Unstable

0.07

0.15

Neutral

0.15

0.25

Very Stable

0.55

0.30

B
EAUFORT

S
CALE


This scale is helpful in getting an idea on the magnitude
of wind speed from real life observations

Atmospheric

condition

Wind speed

Comments

Calm


< 1mph

Smoke rises vertically

Light breeze


5 mph

Wind felt on face

Gentle breeze


10 mph

Leaves in constant motion

Strong


25 mph

Large branches in motion

Violent storm


60 mph

Wide spread damage

W
IND

R
OSE

D
IAGRAM

(WRD)

Wind Direction (%)

Wind Speed (mph)

W
IND

R
OSE

D
IAGRAM

(WRD
)


WRD provides the graphical summary of the
frequency distribution of wind direction and wind
speed over a period of time


Steps to develop a wind rose diagram from hourly observations
are:


Analysis for wind direction


Determination of frequency of wind in a given wind
direction



Analysis for mean wind speed


Preparation of polar diagram


Calculations for Wind Rose


% Frequency =


Number of observations * 100/Total Number of
Observations


Direction: N, NNE,
------------------------
,NNW, Calm


Wind speed: Calm, 1
-
3, 4
-
6, 7
-
10,
-----------



D
ETERMINATION

OF

M
AXIMUM

M
IXING

H
EIGHT


Steps to determine the maximum mixing height for a
day are:


Plot the temperature profile, if needed


Plot the maximum surface temperature for the day
on the graph for morning temperature profile


Draw dry adiabatic line from a point of maximum
surface temperature to a point where it intersects
the morning temperature profile


Read the corresponding height above ground at the
point of intersection obtained. This is the

maximum
mixing height for the day

D
ETERMINATION

OF

M
AXIMUM

M
IXING

H
EIGHT

P
OWER

PLANT

P
LUMES

IN

M
ICHIGAN

Monroe Power Plant

P
OWER

PLANT

P
LUMES

IN

M
ICHIGAN

Trenton Channel

P
OWER

PLANT

P
LUMES

IN

M
ICHIGAN

Belle River Power Plant

River Rouge Power Plant

Photo credit:


Kimberly M. Coburn

PROBLEMS


During an air pollution experiment the lapse rate was a
constant at 1.1
°
C per 100 m. If the atmosphere is assumed
to behave as a perfect gas and the sea level temperature
and pressure were 16
°
C and 1 atm, at what altitude was
the pressure one
-
third the sea level?

S
OLUTION


Step1:



Step 2:

Calculate Temperature


Step 3:



Substitute for temperature


Step 4:

Integrate between P = 1 and P = 0.333, and between z = 0, and z = z.











Z = 7817.13m



R
EFERENCES


Met Monitoring Guide:
http://www.webmet.com/met_monitoring/toc.html


Regulatory Guide


office of nuclear regulatory research:

http://www.nrc.gov/reading
-
rm/doc
-
collections/reg
-
guides/power
-
reactors/active/01
-
023/01
-
023r1.pdf


NOAA
-
National Climate Data Center